New Formulations and Valid Inequalities for the Optimal Power Flow Problem

The optimal power flow (OPF) problem is a nonconvex quadratically constrained continuous optimization problem that is a key problem in the area of electrical power systems operations. The theme of our work is to design algorithmic techniques for finding globally optimal solutions of OPF. We begin by presenting a new formulation for the OPF problem. We prove that the McCormick relaxation of the classical (rectangular) formulation of OPF is weaker than the McCormick relaxation of the new formulation. We present results on the quality of other relaxations such as a second order conic (SOCP)and semi-definite (SDP) relaxation of the new formulation. Then, we present a class of valid inequalities for OPF in the context of the new formulation. Finally, we present extensive computational results to compare the performance of the new formulation and valid inequalities against the performance of the classical formulation. This is joint work with Burak Kocuk and Andy X. Sun.